Directional diffuser

ABSTRACT

A diffuser is disclosed which transmits or reflects incident light into a specific range of angles. In a preferred embodiment, this light is uniformly scattered throughout a cone of angles. The diffuser consists of two parts. The first part diffracts or reflects light into a specific offset angle. The second part, in the preferred embodiment, uniformly scatters the light through a range of angles, which is centered on the offset angle. The diffusers have utility in applications such as screens for wrist watches, computers, calculators, and cell phones.

RELATED APPLICATIONS

This application is a divisional application of U.S. Ser. No.10/639,552, filed Aug. 12, 2003, which is a divisional application ofU.S. Ser. No. 09/920,060, filed Aug. 1, 2001 (now U.S. Pat. No.6,608,722), which claims priority to U.S. Ser. No. 60/222,182, filed onAug. 1, 2000, both of which are incorporated herein by reference.

FIELD OF THE INVENTION

The present invention relates generally to an optical diffuser andmethod for making the same, and more particularly to an optical diffuserhaving a high diffraction efficiency, broadband response and costeffective method of producing the same.

BACKGROUND

Reflective diffusers are required for many applications, includingliquid crystal displays, to enhance their viewability. Often thesediffusers, placed behind the liquid crystal element, are simplyroughened reflective surfaces. These reflectors utilize no backlighting, but instead rely on the scattered reflection of the ambientlight. Unfortunately, light scattered from these devices is centeredaround the glare angle, which is in direct line-of-sight with theundesirable reflections from their front surface. Furthermore in manyapplications, such as computer screens, and perhaps watches, thepreferred orientation of the device is one for which viewing at theglare angle is not optimum. The situation can be improved by usingholographic diffusers which allow the reflection angles of interest tobe offset, so that the maximum brightness from the diffuser falls in apreferred viewing angle which is different from that of the glare. Onetype of holographic diffuser that is sometimes used is the reflective,“surface-relief” hologram. This hologram has the advantage over othertypes in that if the ambient light is white, the reflected diffuse lightis also white. Another advantage of the surface-relief hologram is thatembossing can reproduce it easily and inexpensively. A majordisadvantage is that the surface-relief hologram can be inefficient.Only a relatively small percentage of the incident light is diffractedinto the desired viewing angles (typically less than 30 degrees).

A non-holographic diffuser, when coupled with a reflective focusingscreen, uses randomly sized and randomly placed minute granules, whichare created by interaction of solvent particles on plastic surfaces (SeeU.S. Pat. No. 3,718,078, entitled, “Smoothly Granulated Optical Surfaceand Method for Making Same”). These granules are dimples of extremelysmall magnitude (one half of a micron in depth), which reflect incidentlight more or less uniformly over a restricted angle. However, theangles of reflectance are very small, usually about + or −3 degrees, andthe light reflected from them is here again at the glare angle.

A second kind of off-axis, holographic diffuser in common use today isthe volume reflection diffuser, which can be provided by PolaroidCorporation of Cambridge Mass. With volume holograms, fringes that giverise to the diffuser reflection are distributed throughout the volume ofthe material, unlike the surface reflection concept of the“surface-relief” holograms. Because of this, light of a wavelength thatis characteristic of the spacing distance between the fringe planes isresonantly enhanced over all other wavelengths. Thus, the reflectedlight is highly monochromatic. For example, if the spacing ischaracteristic of green, then green will be the predominant reflectedcolor for incident white light. Unlike conventional embossed holographicdiffusers, the reflection can be extremely efficient, although only overa narrow wavelength band. As a result, the surface-relief hologram canappear dim because most of the incident white light falls outside ofthis select band. Further processing can increase the bandwidth, thusincreasing the apparent brightness, but the resulting diffuser still hasa predominant hue, which is in most cases undesirable. In any event thebandwidth is still somewhat restricted, thus limiting the reflectionefficiency.

Therefore, an unsolved need has remained for a diffuser having a highdiffraction efficiency, broadband response and cost effectivemanufacture, which overcomes limitations of the prior art.

SUMMARY OF THE INVENTION

In an embodiment of the present invention as set forth herein is ablazed diffuser, which includes a reflective surface having a sawtoothstructure. The sawtooth structure includes a series of contiguouswedges, each of which reflects incident oblique light into a beam whichis more or less normal to the gross surface of the device. This wedgestructure may be regarded as simply an off-axis mirror if the wedgespacing (period) is much larger than the wavelength. Superimposed onthis wedge surface is a second structural component, which by itselfdiffracts incident light normal to its surface into rays, whichconstitute only those over a restricted narrow angle (e.g. + or −15degrees). This angle is specified as that which is desired for aparticular application. In an embodiment, this second surface shape isone that uniformly scatters an incident ray throughout the viewingangle. Such a structure gives a so called “flat top” scattering. Whenthese two structures are superimposed, light incident from apredetermined angle which is dependent on the wedge angle, is uniformlyscattered throughout a specified range of viewing angles with a highdegree of efficiency. Almost all incident light is utilized andefficiencies approaching 100% for all visible wavelengths are possible.

In another embodiment, a blazed diffuser is made entirely by optical,holographic means, and it can be fabricated in such a way that thebroadband spectral colors are properly mixed so that the diffractedlight appears white. The recording for this diffuser is done in twoprimary ways. The first is by recording directly from a predetermineddiffuse surface, and the second is by copying from a volume diffuserinto a surface diffuser.

BRIEF DESCRIPTION OF THE DRAWINGS

The foregoing and other objects of this invention, the various featuresthereof, as well as the invention itself, may be more fully understoodfrom the following description, when read together with the accompanyingdrawings in which:

FIGS. 1A, 1B and 1C show a number of embodiments of the diffuser inaccordance with principles of the present invention;

FIGS. 2A, 2B, 2C, 2D, 2E and 2F show a number of embodiments ofreflective surfaces associated with the embodiments of the diffusershown in FIGS. 1A, 1B and 1C;

FIG. 3 shows the flat top diffraction profile of the surface of FIG. 2E;

FIG. 4 shows the diffraction profile of a surface which approximatesthat of FIG. 2E;

FIG. 5 shows the efficiency of light reflected for the structure of apreferred embodiment;

FIG. 6 shows light rays passing into and out the diffuser shown in FIG.1A;

FIG. 7 shows interference fringe planes and the etched surface inphotoresist of an embodiment of the diffuser;

FIG. 8 shows a recording configuration of an embodiment of the diffuserthat uses prism coupling;

FIG. 9 shows a method for copying from a volume diffuser intophotoresist using prism coupling;

FIG. 10 shows a method for making a deep stepped wedge structure byusing a prism coupling;

FIG. 11 shows a recording configuration for adding diffuse reflectanceto a stepped wedge structure using prism coupling;

FIG. 12 shows a recording configuration for making a fine interferencefringe structure parallel to a recording surface by means of prismcoupling;

FIG. 13 shows interference fringe planes and the etched surface inphotoresist of a deep stepped wedge structure; and

FIG. 14 shows a theoretical diffraction efficiency for a ten-step wedgegrating structure with step height=250 nm.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The present invention provides an improved diffuser having a highdiffraction efficiency, broadband response and method for making thesame.

Referring to FIG. 1A, an embodiment of the present invention as setforth herein comprises an improved diffuser including a reflectivesurface. The reflective surface may include a periodic wedge structure1, as shown in FIG. 1A, which reflects incident light 2 so that incidentlight 2 impinges on its surface 3 from an oblique angle, θ, into rays 4which are approximately normal to its surface. These reflected rays 4are contained within a small angular spread if the period p of the wedgeis much greater than the wavelength of the light, λ. It is essentialthat the wedge angle (θ/2) for the surface 3 in FIG. 1A, be selected forthe particular application (e.g. θ/2=15°) and that the period p be largecompared to the wavelength (typically p>100 λ). However, a period thatis too large (>100 microns for example) may be visually annoying. If pis not much larger than λ, then incident light is scattered over otherangles than that normal to the surface, as predicted by diffractionanalysis. Furthermore the angle of scattering is then wavelengthdependent, a feature that tends to detract from a desirable whitediffusion pattern.

Referring further to FIG. 1B, the diffuser further includes a secondstructure 5, which is disposed on the reflective surface. The secondstructure uniformly reflects incident rays across a prescribed angle, α.The surface 6, which is shown in FIG. 1C, accepts an incoming obliquebeam and scatters it uniformly over a range of angles, α. The scatteredbeam is centered on the normal to the structure with high efficiency.The geometry of the second structure 5- or scattering structure, mayitself be periodic with period q, which is smaller than, equal to, orslightly larger than the wedge period p. Such examples of thesestructures are shown in FIG. 2.

There are a variety of surface shapes that may be used for thesestructures. In the present embodiment, a shape for an element of theresulting combined surface can be described by the simple equation:s(x)=ax ² +bx,  (1)where s(x) is the height of the surface and x is the coordinate on thesurface, and an element is defined to span only one peak of thestructure as is shown by the dimension q in FIG. 2. The second term ofequation 1 represents the tilted flat surface on wedge 3. The first termis that of a quadratic, or parabolic reflector, either positive ornegative.

Simple microlens arrays may be approximated by periodic, two-dimensionalparabolic surface arrays and as such have been used successfully tocreate flat top diffraction patterns, i.e., uniform on-axis reflection(or transmission) over a specific range of angles. Theoretically, aplane wave of incident light is uniformly reflected from a periodicsurface throughout a specific range of angles because it has a constantsecond derivative.

In general, the diffraction from any reflective phase surface element,s(x), can include: $\begin{matrix}{{f(\gamma)} \approx {\left( {1/q} \right){\int_{{- q}/2}^{q/2}{{\exp\left\lbrack {2{\mathbb{i}}\quad{s(x)}k} \right\rbrack}{\exp\left\lbrack {{- {\mathbb{i}}}\quad{kx}\quad\gamma} \right\rbrack}{\mathbb{d}x}}}}} & (2)\end{matrix}$where γ is the reflection angle (radians), and k=2π/λ. For example,inserting for s(x) the parabolic function of equation 1, minus the wedge(sawtooth) portion, equation 2 yields $\begin{matrix}{{{\left. {f(\gamma)} \right.\sim{\exp\left\lbrack {{\mathbb{i}}\quad k\quad{\gamma^{2}/8}a} \right\rbrack}}{\int_{t_{1}}^{t_{2}}{{\exp\left( {{- {\mathbb{i}}}\quad\pi\quad{t^{2}/2}} \right)}{\mathbb{d}t}}}}{{{where}\quad t_{1}} = {{{- \sqrt{2{a/\lambda}}}q} + {\sqrt{{1/2}a\quad\lambda}\gamma}}}{{{and}\quad t_{2}} = {{{+ \sqrt{2{a/\lambda}}}q} + {\sqrt{{1/2}a\quad\lambda}\gamma}}}} & (3)\end{matrix}$

The integral in equation 3 is known as the Fresnel integral.

A typical plot of the amplitudes of the diffraction function of equation3, is shown as the dashed curve 7 of FIG. 3. Such curves are derived bydata plotted in cornu spirals, which are a convenient representation ofthese Fresnel integrals. As the size q of the element increases, theundulations evident at the extreme angles are reduced and the curveapproaches the flat top distribution, which is desired for a preferredembodiment. However, this second component of the diffuser structure isperiodic, the periodicity of which is q. For a periodic structure, theangular reflection distribution is punctuated by distinct peaks, thedistance between which is proportional to the wavelength, λ, but isinversely proportional to the element size q. These peaks, whichrepresent the various orders diffracted by the structure, are centeredon the solid lines 10 shown in FIG. 3. The presence of these periodicpeaks need not be detrimental to the diffuser visibility if the period qis large compared to the wavelength, in which case they will be veryclose together, or if the incident light is specularly broad orspatially diffuse, thus obscuring them. For the examples in FIGS. 2A and2B, the elements 11 and 12 are as large as that of the sawtooth, i.e.,q=p, which is an extreme, and perhaps a desirable case, because it alsoreduces the undulations in the envelope (the dashed curve) as discussedbefore.

For parabolic structures, the diffraction function for elements 9 and12, shown in FIGS. 2B and 2D, is slightly different than thatrepresented by equation 3 due to the inverted parabolic function. Theapplicable equation for that surface is $\begin{matrix}{{{\left. {f^{\prime}(\gamma)} \right.\sim{\exp\left\lbrack {{\mathbb{i}}\quad k\quad{\gamma^{2}/8}a} \right\rbrack}}{\int_{t_{3}}^{t_{4}}{{\exp\left( {{- {\mathbb{i}}}\quad\pi\quad{t^{2}/2}} \right)}{\mathbb{d}t}}}}{{{where}\quad t_{3}} = {{{- \sqrt{2{a/\lambda}}}q} + {\sqrt{{1/2}a\quad\lambda}\gamma}}}{{{and}\quad t_{4}} = {{{+ \sqrt{2{a/\lambda}}}q} + {\sqrt{{1/2}a\quad\lambda}\gamma}}}} & (4)\end{matrix}$

The function f′ is the complex conjugate of f (i.e., f′=f*), a resultthat is evident from Fourier analysis, and so the amplitude of f′ isalso represented by the dashed curve 7 of FIG. 3. Here again, a periodicstructure as shown in FIG. 2D, results in peaks represented by the solidlines 10.

The structures 13 and 14 shown in FIGS. 2E and 2F combine the elementsdescribed by equation 3 and equation 4. After addition of suitablerequisite phase terms (to account for lateral shifts and pedestal phasefunctions), these surface components, in the absence of the sawtoothcomponent, give diffraction functions f(γ)f(γ)˜

e{exp [ikγ/2+ika ²/2]f(γ)}  (5)

-   -   where the symbol        e refers to the ‘real part’.

Because of the additional phase terms in equation 5, the dashed curve 10of FIG. 3 represents the maximum diffraction that is achieved.Furthermore, peaks occur in this curve at half the distance of those forthe cases discussed so far, since the period of this combined structureis now 2q versus q previously.

The surface shown in FIG. 2G is particularly interesting. Each elementof FIG. 2A alternates with its inversion shown in FIG. 2B to produce asurface without discontinuities. Each element of width P, is an offsetparabola when equation (1) is applied.

A surface which approximates the undulating parabolic surface of FIG. 2E(disregarding the sawtooth or wedge) is that which is represented by asine or cosine function. Such a function can be constructed from thesurface relief etching of two interfering, coherent beams. A functiondescribing such a surface can include:s(x)≈c sin(πx/q)  (6)where 2c is the peak-to-peak excursion of the function, which isperiodic in 2q. Inserting this function into equation 2 results in thediffraction function $\begin{matrix}{{f(\gamma)} \approx {\int_{- q}^{q}{{\exp \cdot \left\lbrack {2{\mathbb{i}}\quad{kc}\quad{\sin\left( {\pi\quad{x/q}} \right)}} \right\rbrack}{\exp \cdot \left\lbrack {{- {\mathbb{i}}}\quad{kx}\quad\gamma} \right\rbrack}{\mathbb{d}x}}}} & (7)\end{matrix}$

-   -   whose solution is        f(γ_(m))˜J _(m)(2kc)  (8)        where J_(m) is the m^(th) order Bessel function of the first        kind, m is an integer, and f(γ_(m)) represents the amplitude of        the diffracted (or reflected) beams at the discrete angles of        γ=mλ/p. In FIG. 4, discrete values of |f(γ_(m))|², for example        15 and 17, are plotted for the case in which the period 2 q        equals 38λ, and the angular spread is approximately ±15 degrees.        As can be seen in FIG. 4, the profile 16 is not flat-topped, but        peaks at specific angles (17 in FIG. 4). Such peaks tend to be        reduced as the period, 2q, increases with respect to the        wavelength, and a reasonable approximation to a flat top angular        distribution is obtained.

Another method of producing a parabolic surface structureholographically is by the coherent interference of three laser beams ina layer of photoresist. If the sources of expanded light from each ofthe beams are arranged such that each source is approximately at theapex of an equilateral triangle, then the developed pattern in thephotoresist will consist of a close-packed honeycomb array. By usingsuitable nonlinear etching characteristics of the photoresist, eachhoneycomb depression will develop in the shape of a paraboloid.

While the specific examples discussed so far relate to the reflection ofincident light from a surface in air (i.e., n=1), the analysis alsoapplies to cases in which the light is reflected from a surface that iscovered, for example, by a plastic overcoating. In an embodiment, areflective diffuser is provided, which includes a reflective surfacethat is embossed into the underside of a plastic sheet. In thisembodiment, slight modifications to the analysis must be made, mainly inan alteration of the depth of the structure. (In equation 2, forexample, s(x) becomes n s(x), where n is the index of refraction of theplastic). Also certain modifications would enable these devices to beused as transmission diffusers, rather than reflection diffusers.

Construction of surfaces discussed herein, and examples of which areshown in FIG. 1, may be carried out by a number of processes. For welldefined periodic functions like those shown in FIG. 1, the surfaces canbe formed by micro-machining or laser etching (e.g., MEMS processes).Alternatively the surfaces can be formed in two separate steps, whichincludes a first step that produces a periodic sawtooth structure suchas that shown in FIG. 1A. Such a strictly periodic structure can, forexample, be machined with great precision and cast into a number ofmaterials. A second step, which adds the diffusion, or second component,may be added, for example in the following way. After appropriatelycoating the periodic sawtooth structure with a photoresist layer, thediffusing structure may be created by exposure to appropriate opticalpatterns and suitable processing of the photoresist thereafter. Theseoptical patterns may be generated as an interference pattern of a numberof coherent beams (the sine wave for example), the three-beam honeycombpattern as described above, or as a result of scanning the photoresistsurface with a focused intensity modulated light beam (as with a laser).Alternatively the optical pattern to which the photoresist is exposedmay be a random function resulting, for example, from a laserilluminated diffuser. Randomly diffuse functions whose angulardiffraction envelope are flat-topped, are usually difficult to create,unless unique processes are used.

The randomness may be achieved for example by using small portions ofthe prerequisite parabolic surface, which are randomly positioned butwhich on the aggregate cause reflected light to be more or lessuniformly reflected over the desired angle.

Another process, described in the following, is a direct holographicmethod. The structure created by this method is different than thatdiscussed so far, in that the period p is of the same order as thewavelength, λ, and thus diffraction effects become important. FIG. 5illustrates the results of scalar diffraction theory, in which curve 18is the major diffracted order, and the diffraction efficiency approaches100% for the wavelength of interest. The step height h for the caseshown in the FIG. 6 is equal to half the peak wavelength. For a centralwavelength peak of 500 nm, the step height is thus 250 nm. Thisefficiency curve assumes that the surface is an ideal reflector,providing 100% efficiency at the peak wavelength. The efficiencies arealso high for the entire visible spectral range, roughly ranging fromapproximately 85% at 400 nm in the violet to approximately 75% at 700 nmin the deep red. For this reason 500 nm is generally chosen to representthe center of the visible spectrum, and the surface structure isdesigned to operate at this wavelength. Note that there is a significantdifference between the small scale structure represented by curve 18,and the diffraction (or reflection) from the surface 3 of FIG. 1A. InFIG. 1A, the step height is many wavelengths, resulting in a diffractionefficiency of close to 100% for all visible wavelengths.

The parameters of FIG. 5 are chosen for the case of an air interfacebordering the reflective sawtooth surface, similar to the situationshown in FIG. 1A. In the actual case, as with the situation of FIG. 1A,a preferable configuration is the coating of the surface with aprotective layer, usually a clear plastic material 19 having an index ofrefraction, n=1.5, as in FIG. 6. The tilt angle of the sawtooth 3 ischosen to provide an optimum viewing angle normal to the surface whenlight is incident at the proper offset angle, which for illustrativepurposes can be 30 degrees. The wedge angle, β/2, can be selected forthe overcoated surface as shown in FIG. 6. Snell's Law, sin θ=n sin β,for light passing from air with index 1 into a medium with index n,yields, for an entrance angle from air of θ=30 degrees, an exit angle ofβ=19.47 degrees within the n=1.5 surface. The wedge tilt angle is halfthis value, or 19.47/2=9.74 degrees. The revised step height ish=250/n=250/1.5=166.67 nm. The period p is calculated from the gratingequation for normal incidence, β=p sin θ, or p=500/sin 30°=500/(1.5 sin19.47°)=1000 nm=1.0 micron.

One method of creating the periodic wedge is by recording theinterference of two counterpropagating laser beams, 20 and 21 in FIG. 7,in a material 22 such as photoresist (n=1.7). The equation for spacingbetween the interference planes, d, can include:d=λ _(o)[2n sin (θ_(o)/2)]  (9)where θ_(o) is the half angle between the beams, and λ_(o) is the laserrecording wavelength. Thus the sine of the half angle is calculated inaccordance with the following:sin(θ_(o)/2)=λ_(o)(2nd)=441.6/[(2)(1.7)(169.11)=0.76803  (10)where a recording wavelength of λ_(o)=441.6 nm from a He—Cd laser and anindex of refraction of n=1.7 for photoresist have been used. Thespacing, d, has been calculated asd=h/[cos (β/2)=166.67/[cos(9.74°)=169.11 nm  (11)Thus equation 10 yields an angle between the beams of θ_(o)=100.36°. Theinterference fringe structure, 23, is shown in FIG. 7. This structurerepresents, after exposure, planes of maxima and minima of exposureintensity. When the photoresist plate is immersed in developer, etchingor removal of the exposed photoresist proceeds from the top surfacelayer downward, the most exposed layers being removed preferentiallyover the least exposed layers. Ideally, the developer reaches the firstzero exposure plane, which is represented by the dotted line 24 in FIG.7. The fringe planes lying beneath this plane are not affected by thedevelopment.

The preceding discussion represents the types of calculations that mustbe made in order to accurately form the fringe planes, and thus thesawtooth structure in a photoresist material, which is ultimately usedas a master copy for mass production. In an embodiment, at least one ofthe beams, 20 and 21, in FIG. 7, can have some variation so as to createthe desirable angular diffusion.

If there were no diffuse component to the beam, then the lightdiffracted from the sawtooth surface relief structure would, forincident white light, display all the spectral colors from violet tored, although each would be viewable from a different angle. Butcontrolled diffusion is a requirement of this technology. Adding adiffuse component to obtain white light means adding a variation in thegrating period p or in the slope of the sawtooth, so that all colors aremixed at the same diffraction angle. For example, taking the extremes of400 nm for violet and 700 nm for red, the period p for these two colorsis, respectively, p=400/sin 30°=800 nm (violet) and p=700/sin 30°=1400nm (red) for the same diffraction angle of 30 degrees. If these extremesin the period for the visible spectrum are now present as part of thesurface relief structure, then the diffraction angles for the designwavelength of 500 nm range from 38.68 degrees to 20.92 degrees, so thatthe total variation is 8.68+9.08=17.76 degrees. Since the diffuser isnominally designed to operate at an angular spread of plus or minus 15degrees from the main diffraction angle of 30 degrees (or a totalangular spread of 30 degrees), there is sufficient angular variation formixing the entire visible spectrum sufficiently to produce white light.

A method for making the diffuse structure is to use a split beamholographic setup and a predetermined diffuse surface. This methodallows for flexibility in the range of recording angles. The methoddoes, however, require the fabrication of a diffuse plate with therequisite viewing angles, which is inserted into at least one of the tworecording beams. In one configuration, as shown in FIG. 8, requires theuse of two prisms, 25 and 26, with a liquid gate plate holder contactedby index matching liquid to both prisms. The calculated angles for beam20 with respect to the normal, i.e., 49.56 degrees, is so large that itexceeds the critical angle, θ_(c), which is θ_(c)=arcsin (1/n)=arcsin(1/1.7)=36.03 degrees. In the absence of a coupling medium, i.e., an airinterface, all incident light would be at almost normal incidence to theface of the equilateral prism 25. Beam 20 enters the face of theopposite prism 26 such that the angle of incidence to the photoresistmaterial 22 from the n=1.5 glass layer is equal to 34.61 degrees. Inthis case the fringe spacing and tilt angle in the photoresist are asrequired for the example above. Because the angle of incidence of beam20 does not exceed the critical angle into photoresist, an alternativescheme allows beam 20 to enter the tank directly from air at 58.43degrees, A third alternative is one in which the rectangular plateholder tank is immersed in a large square tank filled completely withindex matching liquid, thus eliminating the prisms altogether. Whilethis latter method is relatively easy to implement it does require greatcare in allowing the index matching liquid to completely stabilizebefore making the recording.

Copying directly from a volume diffuser, as an alternative to the above,has many advantages. One advantage relates to a volume diffuser with therequisite offset and viewing angles, which can be efficiently producedholographically. Another advantage relates to the copying procedure,which is simpler than direct recording using a predetermined diffusemaster, provided certain conditions are met. One of these conditions isthat the peak wavelength of light diffracted from the master fallsroughly into the center of the visible spectral range. Also the volumediffuser, which is used for copying, can have the proper angular spreadto create an adequate viewing angle in the reflective mode.

A method of forming a structure like that of FIG. 7 from a volumehologram is shown in FIG. 9. In order to form such a structure we assumethat (1) photoresist 22, is in intimate contact with the holographicdiffuser 27, (2) beam 21 is incident from outside, passing through thephotoresist and into the volume hologram, (3) beam 20 is reflected fromthe interference planes 28 within the volume hologram back through thephotoresist layer and (4) the index of refraction of the volume hologramhas a typical value of n=1.5. Thus copying is done with only a singlebeam.

In order to create beams 20 and 21 at angles of 49.56 degrees and 30.08degrees (as shown in FIG. 7), these beams, denoted as 29 and 30 in FIG.9, must have angles of 59.61 degrees and 34.61 degrees respectively inthe lower index material 27 (n=1.5). Such beams exist in the volumereflective hologram 27 only if it contains fringe planes tilted at 12.5degrees as shown in FIG. 9, and whose spacing d=216.28 nm. This assumesthat the copy wavelength is 441.6 nm. Light incident normally onto thesefringe planes will reconstruct coherently at a wavelength ofλ=2nh=2(1.5)(216.28)=648.85 nm, which is red. This result points out afundamental characteristic of this type of construction; namely, thatcopying into a high index material at large incidence angles from alower index master, requires that the master be red-shifted with respectto the copy. In other words, reconstruction of a blazed surface patternproducing light peaked in the green spectral region requires a masterpeaked in the red spectral region. Such a volume hologram can be easilymade with a conventional holographic setup using red laser light (e.g.,a Kr laser at 647 nm or a He—Ne laser at 633 nm) and eitherred-sensitive photographic emulsion or photopolymer. It is also possibleto copy from a photopolymer master diffuser that is already tuned to thegreen spectral region, provided that certain steps are made to convertthe diffuser to the red region. For example, the green Polaroid Imagixdiffuser photopolymer can be copied directly into a DuPont 706photopolymer, using either green laser light at near normal incidence orblue 441.6 nm laser light at a large angle of incidence. The DuPontmaterial can then be tuned to the red region using DuPont CTF colortuning film, which essentially swells the photopolymer to a largerthickness, thereby increasing the spacing between the planes andchanging the color from green to red.

Here again the angle for beam 20 in the photoresist is greater than thecritical angle (49.56>36.03) and we must resort to coupling by means ofa liquid gate. The photoresist plate is placed in a rectangular tankcontaining an index matching liquid for glass at n≈1.5 (e.g., xylene)that is liquid coupled to an equilateral prism, as shown in FIG. 9.

Variations of the methods disclosed here can result in efficientdirectional diffusers. For example, with the first type disclosed,uniform angular spreading of the incident beam may be accomplished by avariation of either the period p or the slope θ/2 from sawtooth elementto sawtooth element. However, such a procedure may require that theelement size p be reduced (for example from 100 λ to 10 or 20 λ) so asto preserve the smooth visual texture of the diffuser. If the size p istoo large, visible portions of the diffuser will not scatter into theobservation direction.

A variation of the holographic method discussed herein, is the additionof a fine diffusing structure to a coarse wedge structure. This coarsewedge structure is of larger dimensions than that of the methodsdescribed in FIGS. 7 and 8, and can be constructed in the followingmanner, as shown in FIG. 10. Two beams enter the photoresist layer 33that is coated onto a glass substrate 34 from the same side 35 at anoblique angle, such that the interference fringe structure 36 is coarseand inclined at some angle with respect to the surface. Prism couplingallows for a large degree of obliquity in a manner similar to that shownin FIG. 9.

A diffuse component can be added in a second exposure step by contactingthe photoresist layer 33 to a reflective diffuser 39, as shown in FIG.11. In this case the incident beam 37 is totally reflected as a diffusebeam 40 that encompasses a range of angles. The contact can be doneusing either a liquid gate, or by reversing the plate and attaching thediffuser directly to the glass substrate and using a liquid gate betweenthe photoresist and the prism. For this procedure to be effective, theresist should be coated to a several micron thick layer. The firstexposure should be done at a laser wavelength for which absorption islarge, for example 441.6 nm, so that the amount of reflected light isminimal. The second exposure should be done at a longer, less absorbingwavelength, for example 457.9 or 476 nm, so that the reflected beam isnearly equal in intensity to the incident beam.

An alternate technique adds a fine step structure to the coarse wedge ofFIG. 10, in place of the fine diffusing structure. With this techniquethe second exposure uses two beams that enter the photoresist fromopposite sides so that the interference fringe structure is fine andparallel to the surface. This is also done by prism coupling, using asingle beam 37 that is totally reflected that interferes with itself, asshown in FIG. 12, with the fine fringe structure designated as 38. Forthis exposure the photoresist plate is reversed so that the surface 35faces out. When the photoresist is developed after the compositeexposure, the resulting structure is a deep wedge-shaped grating thathas a fine stepped grating superimposed onto it (FIG. 13).

The diffraction efficiency for a ten-level structure is shown in FIG. 14and includes the spectral distribution for diffracted orders +2, +1, 0,−1, and −2. Also included in this plot is the spectral distribution fora single-step blazed grating, which is identical to FIG. 5. It isclearly evident that the spectral distribution for the single-stepshallow blazed grating forms an envelope for the ten-level deep steppedgrating. The number of orders that appear under this envelope decreasesas the number of levels is reduced, but their individual spectral widthincreases.

As can be seen from FIG. 14, the diffraction is specularly discrete,allowing only narrow band color components to be observed at any givenviewing angle. In order to avoid this often undesirable result, thephotoresist can be exposed in narrow adjacent stripes that yield, forexample, red, blue, and green light diffracted at the same angle toproduce white. The proper angle for light diffracted from the steppedgrating structure is determined by the periodicity of the coarse wedgegrating, and that periodicity depends, in turn, on the oblique anglethat the interference fringe structure makes with respect to thephotoresist surface.

Another variation on this method consists of first making a wedgegrating structure of large periodicity and adding the step structure ordiffuse structure to it holographically. In this configuration, it issimilar to the structure shown in FIG. 1 c. For the step structure, theprocedure consists of coating the wedge structure with a thin, uniformlayer of photoresist, which can be done either by dip coating or by spincoating. The coated wedge surface is then immersed in an index-matchingliquid gate that is optically contacted to an equilateral glass prism,as described above. The step structure is made by exposing to a totallyreflecting beam of laser light that is coupled to a diffuse surface,also described above. With this method many more diffracted orders areobtained than with the totally holographic method described above, dueto the much greater depth of the preformed structure compared to thatobtained holographically, but with diffuse mixing the diffracted lightappears white.

The discussion has focused on devices that uniformly scatter lightthrough a solid angle. But in some applications it may be desirable toachieve non-uniform scattering. One can modify the processes to createblazed diffusers that have a wide range of scattering properties.

Both categories of structures have been described in the foregoing inreference to their scattering properties in one dimension only. That is,the emphasis has been on showing how an incident beam whose obliquity tothe surface (i.e., θ=30°) is scattered uniformly throughout an angle α,as in FIG. 1. But in the other direction, which follows the coordinategoing into the paper in all of the Figs., the illumination beam 2 (SeeFIG. 1) is assumed to have no obliquity, but to impinge perpendicular tothe surface. In order to obtain a uniform angular diffusion, there is asimilar requirement for scattering over an angle of α in this dimensionalso, albeit without an offset θ. For the first category of diffuserdescribed here, the surface profile into the paper for the surface ofFIG. 2 would contain the parabolic component, thus providing a diffuser,each portion of which scatters uniformly throughout a pyramidal solidangle which is offset from the incident illumination by angle θ.Similarly if a beam, which is randomly diffuse throughout a cone ofangles, is reconstructed as beam 20 in FIG. 9 from the photopolymerhologram 27, the resulting aluminized diffuser will scatter incominglight throughout a conical solid angle, offset by angle θ.

Having thus described at least one illustrative embodiment of theinvention, various alterations, modifications and improvements willreadily occur to those skilled in the art. Such alterations,modifications and improvements are intended to be within the scope andspirit of the invention. Accordingly, the foregoing description is byway of example only and is not intended as limiting.

1-15. (canceled)
 16. A method for making a directional reflector havinga reflective surface, wherein the reflective surface includes at leastone periodic surface comprising a plurality of periodic surface piecesand wherein the period surface pieces are each described by a parabolicfunction and reflect an incident ray throughout a specified uniform coneof angles, comprising the steps of: creating a gray scale mask;transmitting recording light through the gray scale mask such that adesired parabolic function is displayed; and recording the desiredparabolic function in a layer of photoresist.
 17. The method for makinga directional reflector having a reflective surface of claim 16, furthercomprising the step of coating a second periodic surface with the layerof photoresist prior to recording the desired parabolic function. 18.The method for making a directional reflector having a reflectivesurface of claim 17, wherein the second periodic surface iswedge-shaped. 19-20. (canceled)
 21. A method for making a directionalreflector for reflecting an amount of incident light, the directionalreflector having a reflective surface, wherein the reflective surfacehas a periodicity on the order of a wavelength of the incident light andwherein the reflective surface further includes a coarse periodicityhaving an asymmetrical blazed profile and a fine periodicity, comprisingthe steps of: creating the coarse periodicity having an asymmetricalblazed profile by prism coupling and recording into a layer ofphotoresist using more than one beam, wherein each beam is separated bya small angle and wherein each beam is incident at a large obliqueangle; and creating the fine periodicity by reflecting a single beamfrom the layer of photoresist using prism coupling.
 22. The method formaking a directional reflector having a reflective surface of claim 21further comprising the step of adding a diffuse component by having onebeam be incident through the photoresist layer onto a predetermineddiffuse reflector by means of prism coupling.
 23. A method for obtainingwhite light using a directional reflector having a reflective surface,wherein the reflective surface has a periodicity on the order of awavelength of incident light and wherein the reflective surface furtherincludes a coarse periodicity having an asymmetrical blazed profile anda fine periodicity, comprising the steps of: creating the coarseperiodicity having an asymmetrical blazed profile by prism coupling andrecording into a layer of photoresist using more than one beam, whereineach beam is separated by a small angle and wherein each beam isincident at a large oblique angle; creating the fine periodicity byreflecting a single beam from the layer of photoresist using prismcoupling; and recording the fine periodicity in adjacent narrow parallelstripes, wherein each stripe reflects a different color.
 24. A methodfor making a directional reflector having a reflective surface, thereflective surface comprising a first periodic surface component havinga periodic wedge-shape, the periodic wedge-shape having a first periodand a second periodic surface component, the second periodic surfacecomponent having a second period, wherein the combination of the firstperiodic surface component and the second periodic surface componentcause an oblique light ray, which is incident on the reflective surface,to be reflected into a cone of rays, comprising the steps of:mechanically ruling the wedge-shape; creating a plastic replica from themechanical ruling; creating a random array of shallow parabolicdepressions by spraying the plastic replica-with a fine droplet spraycontaining a plastic solvent.
 25. The method for making a directionalreflector having a reflective surface of claim 24, further comprisingthe steps of: creating a metal replica from the sprayed plastic replica;creating a second plastic replica from the metal replica; and sprayingthe second plastic replica with a fine droplet spray containing aplastic solvent.
 26. The method for making a directional reflectorhaving a reflective surface of claim 25 wherein the steps are repeated.